Band-limited adaptive feedback canceller for hearing aids

ABSTRACT

An improved method for adaptively cancelling acoustic feedback in hearing aids and other audio amplification devices. Feedback cancellation is limited to a frequency band that encompasses all unstable frequencies. By limiting the bandwidth of the feedback cancellation signal, the distortion due to the adaptive filter is minimized and limited only to the unstable feedback regions. A relatively simple signal processing algorithm is used to produce highly effective results with minimal signal distortion.

RELATED APPLICATION

This application claims the benefit of co-pending provisionalapplication Ser. No. 60/102,557 filed Sep. 30, 1998.

This invention was made with government support under grant #R01DC03825awarded by the NIH National Institute for Deafness and otherCommunication Disorders (NIDCD). The government has certain rights inthe invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to the field of audioamplification, especially for hearing aids. More particularly, theinvention provides a method for efficiently cancelling acoustic feedbackin the hearing aid.

2. Prior Art

Acoustic feedback in a hearing aid, from the electroacoustic transducer(commonly referred to as the “receiver”) back to the microphone, iscommon and difficult to suppress. Feedback may produce an audiblewhistle, which is irritating to the hearing aid wearer so that thewearer must often reduce the volume to a lower than desired level,thereby reducing the effectiveness of the hearing aid.

One reason that it is difficult to effectively suppress acousticfeedback in a hearing aid is that the frequency at which feedback occursvaries with changing external conditions. Therefore, for feedback to beeffectively cancelled without undesirably degrading the amplifiedsignal, some form of adaptive cancellation is required. Varioustechniques have been proposed for implementing adaptive feedbackcancellation. Such techniques are disclosed, for example, in U.S. Pat.Nos. 5,016,280; 5,091,952 and 5,259,033.

One of the principal design objectives for hearing aids isminiaturization of physical volume. Most wearers prefer a hearing aidthat can be worn entirely within the ear. Advances in microelectronicshave vastly improved the signal processing capabilities of in-the-ear(ITE) hearing aids. Even so, the provision of effective feedbackcancellation remains a practical design challenge. Prior art techniquesnecessarily require certain trade-offs. As a result of such trade-offs,the hearing aid may exhibit only a small increase in maximum stablegain, slow filter adaptation, distortion, interference and/or lack ofadaptation to individual wearers.

SUMMARY OF THE INVENTION

The present invention provides an improved method for adaptivelycancelling acoustic feedback in hearing aids and other audioamplification devices. Feedback cancellation is limited to a frequencyband that encompasses all unstable frequencies. By limiting feedbackcancellation in this manner, a relatively simple signal processingalgorithm may be used to produce highly effective results with minimalsignal distortion.

In order to implement the present invention, unstable feedbackfrequencies must first be identified. This is accomplished by varioustechniques with real ear measurements, from which the complex open looptransfer function may be derived. Once the unstable feedback frequenciesare identified, a band limited adaptive filter is implemented. By thuslimiting the bandwidth of adaptation, the adaptive feedback canceller isable to adapt very quickly within the range of unstable frequencies withrelatively low adaptation noise. By limiting the bandwidth of thefeedback cancellation signal, the distortion due to the adaptive filteris minimized and limited only to the unstable feedback regions. Comparedto broadband feedback cancellation, the band limited feedback cancellerof the present invention produces less distortion, and therefore theoutput sound quality is much improved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of a hearing aid in which thepresent invention may be implemented.

FIG. 2 is a simplified diagram illustrating the transfer functions ofthe hearing aid of FIG. 1.

FIG. 3 illustrates a prior art technique for deriving the open looptransfer function of a hearing aid.

FIG. 4 is a functional block diagram of a hearing aid which incorporatesa generic broadband adaptive feedback canceller.

FIG. 5 is a functional block diagram of a hearing aid having an internalnoise generator for derivation of the open loop transfer function.

FIG. 6 is a functional block diagram of one embodiment of a hearing aidhaving a band-limited adaptive feedback canceller in accordance with thepresent invention.

FIG. 7 is a functional block diagram of another embodiment of a hearingaid having a band-limited adaptive feedback canceller in accordance withthe present invention.

FIG. 8 illustrates base-2 logarithm quantization as used by the presentinvention for filter coefficient adaptation.

FIG. 9 is a functional block diagram illustrating the signal processingused to implement an adaptive digital filter.

FIG. 10 illustrates the processing used for power estimation.

FIG. 11 illustrates the processing used for coefficient adaptation.

FIG. 12 illustrates the processing used for DC removal.

FIG. 13 illustrates the processing used for bandpass filtering.

FIG. 14 is a functional flow diagram illustrating the process schedulingimplemented by the control unit of FIG. 9.

FIG. 15 is a logic diagram corresponding to the flow diagram of FIG. 14.

FIG. 16 is a functional block diagram of an alternative embodiment ofthe present invention.

FIG. 17 is a functional block diagram of another alternative embodimentof the present invention.

FIG. 18 is a functional block diagram of still another alternativeembodiment of the present invention.

FIG. 19 is a functional block diagram of yet another alternativeembodiment of the present invention.

FIG. 20 is a functional block diagram of adjustable FIR filtering with apower-of-two scaling gain.

FIG. 21 is an example of open loop transfer function and unstablefeedback frequencies measured on KEMAR ear.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, for purposes of explanation and notlimitation, specific details are set forth in order to provide athorough understanding of the present invention. However, it will beapparent to one skilled in the art that the present invention may bepracticed in other embodiments that depart from these specific details.In other instances, detailed descriptions of well-known methods anddevices are omitted so as to not obscure the description of the presentinvention with unnecessary detail.

FIG. 1 is a functional block diagram of a hearing aid 10 in an ear of ahearing aid user. The hearing aid 10 comprises a microphone 12,microphone pre-amplifier circuitry 14, analog-to-digital converter 16,signal processing circuitry 18, digital-to-analog converter 20 andreceiver 22. The signal processing circuitry 18 has a transfer functionfrom point C to point D of K(f). The feedback path from point D to pointC includes digital-to-analog converter 20, hearing aid receiver 22,acoustic and mechanical coupling between the receiver and microphone,analog conditioning circuitry 14, and analog-to-digital converter 16.β(f) is the transfer function of the feedback path.

FIG. 2 shows a simplified hearing aid model in the ear. The open looptransfer function of the hearing aid is defined as K(f)β(f). A hearingaid may produce unstable feedback only at those frequencies, f_(u),where its open loop transfer function meet the Nyquist instabilitycriteria: $\begin{matrix}{{{Magnitude}:{{{{K\left( f_{u} \right)} \cdot {\beta\left( f_{u} \right)}}} \geq 1}}\quad{{{Phase}:{{\angle K}\left( f_{u} \right){\beta\left( f_{u} \right)}}} = {n \times 360{^\circ}}}} & {{Equation}\quad 1}\end{matrix}$When the above phase condition is met and the magnitude of the hearingaid open loop transfer function is close to but less than unit gain, thehearing aid is in a sub-oscillatory state. Both sub-oscillation andoscillation are unpleasant to hearing aid wearers and must beeliminated. In the following description, We refer both unstablefeedback frequency and sub-oscillatory frequency as unstable feedbackfrequency. An efficient feedback cancellation algorithm needs to operateonly in the frequency region containing all f_(u). We have found thatwhen feedback cancellation is limited to this frequency region, arelatively simple algorithm can produce highly effective results withminimal signal distortion. None of the previously developed methods offeedback cancellation in hearing aid systems has exploited thisdiscovery.

To derive the open loop transfer function, conventional prior artmethods break the closed loop system after the microphone pre-amplifierand before the hearing aid processing module, as shown between points Cand D in FIG. 3, and make a standard two-channel transfer functionmeasurement with a signal analyzer. However, these methods cannot beconveniently used with commercial hearing aids, because it isimpractical to break the hearing aid circuit. We have developed thefollowing three methods to derive the open loop transfer functionwithout breaking the hearing aid circuit.

The first method utilizes a probe microphone to accurately derive theopen loop transfer function K(f)β(f) from a closed loop measurement byacquiring the probe microphone signals near the eardrum with the hearingaid in the ear canal. This method is described in co-owned patentapplication Ser. No. 08/926,320, the specification of which isincorporated herein by reference. Briefly, the method requires acquiringprobe microphone signals near the eardrum to compute the open looptransfer function with the hearing aid in three gain settings, G1, G2,and G3, where G3=0 (i.e., the hearing aid is off). The method andprocedure of detecting and digitizing the acoustic signal with a probemicrophone used in the current invention are, in part, the subjects ofco-owned U.S. Pat. No. 5,325,436, “Method of Signal Processing forMaintaining Directional Hearing with Hearing Aids”.

The complex open loop transfer function K(f)β(f) can be derived as:$\begin{matrix}{{{K(f)}{\beta(f)}} = \frac{{{G1} \times {H_{2{AB}}(f)}} - {{G2} \times {H_{1{AB}}(f)}} + {{H_{3{AB}}(f)} \times \left( {{G2} - {G1}} \right)}}{{G2} \times {G1} \times \left\lbrack {{H_{2{AB}}(f)} - {H_{1{AB}}(f)}} \right\rbrack}} & \text{Equation~~2}\end{matrix}$where H_(1AB)(f), H_(2AB)(f) and H_(3AB)(f) are closed loop transferfunctions from point A to point B in FIG. 1 measured with G1, G2 and G3.Point A is at the hearing aid microphone input and point B is at thehearing aid receiver output, i.e., at the probe microphone.

Because the probe microphone must be used for the closed loopmeasurements, the venting system of the hearing aid is partially blockedby the probe tube. The derived open loop transfer function is thus onlyan approximation of the open loop transfer function with an open hearingaid vent. The closed loop transfer function measurements are alsosensitive to head movement and surrounding environmental changes duringthe measurements.

The second method does not require a probe microphone measurement. Itrequires configuring the adaptive feedback canceller in the hearing aidto operate in a broadband mode as shown in FIG. 4. The adaptive digitalfilter (ADF) 30 in the hearing aid provides an estimation of thefeedback path including the digital-to-analog converter 20, the receiver22, the coupling path between the receiver and microphone, themicrophone 12, the AGC 14, and the analog-to-digital converter 16.

Data is collected with the hearing aid wearer seated in a quiet room. Awhite noise signal is generated in the sound field through aloudspeaker. The hearing aid is programmed with a known referenceresponse. The hearing aid wearer is instructed to adjust the hearing aidgain below the Uncomfortable Level (UCL). While the white noise isplaying in the sound field, the ADF in the hearing aid adapts itself tomatch the feedback path. After the ADF has converged, the filtercoefficient vector W(n) is read from the hearing aid together with the“delay”. The feedback transfer function β′(f) can be estimated asfollows:β′(f)=e^(−j2πfD) ×W _(n)(f)  Equation 3where D is the delay introduced by “Delay” block 32; W_(n)(f) is thefrequency response of the ADF at time index n, for which the impulseresponse is W(n). To improve the accuracy of the measurement, severalcoefficient vectors W(n_(i)) with different time index n_(i), can beobtained from the ADF and averaged to compute W_(n)(f) in Equation 3.

In order to compensate for the hearing loss of each individual, thehearing aid reference response used during the measurement is replacedby a desired hearing aid response K(f). The complex open loop transferfunction associated with the desired hearing aid response K(f) can beestimated by K(f)β′(F):K(f)β′(f)=e^(−j2πfD) ×W _(n)(f)×K(f)  Equation 4

The unstable feedback frequencies can then be determined by theestimated open loop transfer function based on Equation 1. Comparingwith the first method, this method does not require a probe microphonemeasurement. Therefore, the venting system of the hearing aid is notblocked during the measurement. The measurement is not sensitive to headmovement and surrounding environmental changes. It does not requireadditional circuitry in the hearing aid to support the measurement. Thewhite noise signal serves as a test signal for the measurement, but italso acts as interference noise to the ADF since the signal directlyfrom the loudspeaker does not carry any information about the feedbackpath. Thus, it introduces adaptation noise to the ADF coefficients. Toachieve the best results, the level of the white noise signal should bekept as low as possible but above the noise floor of the room. Thehearing aid gain should be set as high as possible but below UCL andwithout audible feedback. Furthermore, the hearing aid is configured ina closed-loop during the measurement. The unstable feedback rather thanthe UCL may be the limiting factor for setting the hearing aid gain.

The third method is similar to the second method discussed above. Aninternal pseudo-random noise generator as shown in FIG. 5 is used toreplace the external white noise test signal, and the hearing aidprocessing block is disconnected. This method has two advantages overthe second method discussed above: (1) the adaptation interferenceintroduced by the external test signal is removed by using an internalpseudo-random noise generator; and (2) the hearing aid is operated in anopen-loop configuration during the measurement. Thus, the hearing aidgain can be set as high as possible without instability problems. Thismethod requires adding a noise generator and some control logic to thehearing aid. The open loop transfer function measurement is onlyrequired during the initial fitting process.

FIGS. 4 and 5 both illustrate a generic broadband adaptive feedbackcanceller. A digital feedback cancellation signal is generated bypassing the hearing aid digital output signal at point B to an ADF 30,which approximates the feedback path β(f). The digital feedbackcancellation signal is subtracted from the digitized microphone outputat point C, eliminating the feedback signal from the hearing aid.

The ADF 30 comprises an adjustable filter, which uses filtercoefficients to generate a feedback cancellation signal. A coefficientadaptation portion 34 adjusts the filter coefficients to approximate thefeedback path. There are various adaptive filtering methods, which havedifferent filtering structures and different adaptation algorithms. Someof them exhibit extremely good convergence behavior and accuracy, butrequire extensive computation. For example, the family of Least-Squares(LS) algorithms belongs to this category. For the application ofadaptive feedback cancellation to hearing aids, the simpleStochastic-Gradient (SG) algorithms are sufficient to provide acceptableperformance. The simplicity of the adaptive filtering algorithm is avery important factor for hearing aid applications since it is desirableto minimize the hardware requirements. We choose an FIR(Finite-Impulse-Response) filter with Normalized Least-Mean-Square (LMS)algorithm for the ADF coefficient adaptation because of its simplicityand satisfactory convergence performance. To make the adaptive filteringalgorithm more specifically suitable for the problem of adaptivefeedback cancellation in hearing aids, we adopted a Normalized LMSalgorithm with the adaptation step-size normalized to ADF input anderror, as discussed below.

In general, the adaptive filter is a time-varying system, which cantrack the time-varying feedback paths. But unnecessary variations due tothe adaptation noise of the adaptive filter may also introduceunpleasant distortion in the hearing aid output. Thus, the adjustment ofthe adaptive filter should be minimized except as necessary foreliminating the unstable feedback.

The signals coming from external sound sources (external input signals),other than the signals which are fed back from the hearing aid output tothe hearing aid microphone, are usually considered as an interference tothe adaptation of the adaptive filter. An external input signal normallyintroduces bias to the optimal solution for the adaptive filter. Thebias varies when the external input signal's property changes. Theexternal input signal also causes misadjustment noise during theadaptation process. By removing the frequency components that areunlikely to have potential oscillation problems (unstable andsub-oscillatory) from the adaptation signals: e(n) and x(n), which areused for the adaptation process, the interference effects of theexternal input signal on the adaptation process can be greatly reduced.

For the modified Normalized LMS algorithm, the convergence speed of theadaptive filter is governed by the adaptation step-size, which isinversely proportional to the combined signal power of e(n) and x(n).Reducing the combined signal power would lead to a larger adaptationstep-size, which in return increases the convergence speed. Since we areremoving the components that are irrelevant to the oscillation problemsfrom the adaptation signals, the combined signal power of e(n) and x(n)is reduced so that a larger adaptation step-size may be used to increasethe convergence speed. With a higher convergence speed, the feedbackcanceller can better track the dynamic feedback path and the sudden gainchange of AGC due to a sharp transition of input signal.

Furthermore, due to the recursive topology used in the adaptive feedbackcancellation, the periodicity in the external input signal would causethe cancellation of original signal (external input signal) at thehearing aid output. By removing the frequency components that areirrelevant to the oscillation problems from the adaptation signals, theperiodicity in the adaptation signals, which originates from theexternal input signal, can be reduced. Therefore, the problem ofcanceling the original input signal at the hearing aid output will berelieved.

In addition, the adaptive filter always functions better at frequencieswhere large energy exists. This means that the adaptive feedbackcanceller actively works at oscillation frequencies only when the energyof the oscillation components existing in the adaptive filter inputsignal and the error signal is comparable or greater than the peakenergy of the spectrum of external input signal. As a result, themagnitudes of the frequency components at unstable feedback frequenciesare build up and then suppressed, up and down, around the levels of theexternal input spectral peaks. This is so-called modulation effect ofresidual oscillation components.

By removing the unnecessary frequency components from the adaptationsignals, the peak spectral level is much reduced. Therefore, themagnitudes of the residual oscillation components are also significantlyreduced.

This concept of removing unnecessary frequency components from theadaptation signals is extremely important and beneficial when theexternal input signal is a speech signal. As is well known, speechcontains most of its energy and periodicity at the low frequencies, atwhich unstable feedback is unlikely to occur. Therefore, the lowfrequency components of speech are considered unnecessary for theadaptive filtering and can be easily removed by applying a highpass (orbandpass) filter to the adaptation signals. The cutoff frequency of thehighpass filter is normally set at 200 Hz below the lowest unstablefeedback frequency.

As indicated above, the unstable feedback only occurs at certainfrequencies. To effectively suppress oscillation at these frequencieswithout introducing distortion at other frequencies, the currentinvention configures the adaptive feedback canceller in such a way thatit limits the bandwidth of adaptation signals to the frequency regionsknown to contain the oscillation frequencies. By doing so, the adaptivefeedback canceller adapts very quickly in the oscillation frequencyregions with much less adaptation noise and adapts very slowly in otherregions. As a result, the feedback cancellation signal generated by theADF is also limited to the same frequency regions. Therefore, unlike thebroadband scheme, the band-limited feedback canceller produces lessdistortion, and hence the output sound quality is much improved.

FIG. 6 shows one possible structure to implement the band-limitedadaptive feedback canceller. BPF1 and BPF2 are bandpass filters, whichonly pass the frequency region containing all the unstable feedbackfrequencies. BPF1 and BPF2 remove most of the unnecessary frequencycomponents from e(n) and x(n) to improve the adaptation process. Thehearing aid input signal is filtered by BPF2 and then used as thedesired signal for the adaptive filtering so that the adaptive filteronly generates the cancellation signal in the passband of BPF2. AΔ₂-delay linear-phase FIR filter is selected as the bandpass filter BPF2so that we can use a pure delay Δ₂ to ensure the unfiltered hearing aidinput d(n−Δ₂) is properly time-aligned with the filtered desired signald′(n) at the cancellation junction SUM2 without introducing phasedistortion in the primary hearing aid signal path. Since the additionaldelay Δ₂ in the primary hearing aid signal path may increase the numberof oscillation frequencies and shift the oscillation frequency to alower frequency, the filter length of BPF2 must be minimized. TheΔ₁-sample delay in front of filter BPF1 is used to ensure the feedbackcancellation signal is properly time-aligned with the feedback signal sothat the impulse response of the adaptive filter contains most of theenergy of the estimated impulse response of the feedback path. On theother hand, the delay introduced by the filter BPF1 must not be too longor the cancellation signal generated by the adaptive filter may lagbehind the feedback signal. The group delays introduced by each blockmust meet the following condition:D _(Δ) ₁ (f)+D _(BPF1)(f)+D _(ADF) _(—) _(FIR)(f)=Dfeedback path(f)+D_(BPF2)(f)  Equation 5The optimal delay Δ₁ in samples can be determined based on themeasurement of the feedback path during the hearing aid fitting process.In order to utilize all the ADF coefficients, the delay caused by theadaptive filter should be minimized. The delay Δ₁ must meet thefollowing condition:D _(Δ) ₁ (f)≦D _(feedback path)(f)+D _(BPF2)(f)−D _(BPF1)(f)  Equation 6We choose:Δ₁=min{D _(feedback path)(f)+D _(BPF2)(f)−D_(BPF1)(f)}_(fεpassband)−ε  Equation 7Where ε is the tolerance in samples. We typically choose ε equal to 2.

The output of the ADF is calculated one sample at time. At time index n,the calculation for the M-tap ADF output is described as:$\begin{matrix}{{y(n)} = {\sum\limits_{k = 0}^{M - 1}\quad{{w_{k}(n)} \cdot {x\left( {n - k} \right)}}}} & \text{Equation~~8}\end{matrix}$where {w₀(n), w₁(n), . . . , w_(m−1)(n)} are the coefficients of theM-tap ADF at time index n.

The coefficients of the ADF are updated with a modified Normalized LMSalgorithm. As in the conventional Normalized LMS algorithm, theadaptation step-size is reduced when the signal level is high and viceversa. In feedback cancellation for hearing aids, however, the inputsignal of the ADF is delayed by the hearing aid processing module, BPF1and Δ₁. The power of the error signal e(n) is included for calculatingthe time-varying step-size as follows:e(n)=d′(n)−y(n), where d′(n) is the output of the bandpass filterBPF2  Equation 9

p(n)=p·(n−1)+x ²(n)+e ²(n)  Equation 10 $\begin{matrix}{{\mu(n)} = \frac{C}{\left\lbrack {{\left( {1 - \rho} \right) \cdot {p(n)}} + {ME}} \right\rbrack \cdot M}} & \text{Equation~~11}\end{matrix}$

where ρ is the forgetting factor;

-   -   C is a constant to control the adaptation speed; and    -   ME is a small number to prevent the singularity of μ(n).        The coefficients of the ADF for the next time index n+1 are        updated as follows:        w _(k)(n+1)=w _(k)(n)+μ(n)·e(n)·x(n−k), for 0≦k≦M−1  Equation 12        Due to the bandpass characteristics of BPF1 and BPF2, the        adaptation signals e(n) and x(n) only contain the frequency        components in the oscillation frequency regions.

FIG. 7 shows another possible structure for implementing an adaptiveband-limited feedback canceller. BPF1 is mainly used to limit thebandwidth of the cancellation signal and to limit cancellation artifactsto the cancellation bandwidth. BPF2 and BPF3 are used to limit thebandwidth of the adaptation signals to the oscillation frequencyregions. BPF1, BPF2 and BPF3 are not necessarily implemented aslinear-phase FIR filters, but their passbands must cover all theoscillation frequencies.

The filtered adaptation signal samples are used for updating thetime-varying step-size and ADF coefficients as follows:

p(n)=ρ·p(n−1)+x′² ⁽ n)+e′ ²(n)  Equation 13 $\begin{matrix}{{\mu(n)} = \frac{C}{\left\lbrack {{\left( {1 - \rho} \right) \cdot {p(n)}} + {ME}} \right\rbrack \cdot M}} & \text{Equation~~14}\end{matrix}$  w_(k)(n+ 1)=w _(k)(n)+μ(n)·e′(n)·x′(n−k), for0≦k≦M−1  Equation 15

where x′ (n) is the output of the bandpass filter BPF3; and

-   -   e′ (n) is the output of the bandpass filter BPF2.

To make the adaptive system stable, the phase responses of BPF2 and BPF3must be as close as possible. For simplicity and better adaptation, weselect two identical high pass filters for BPF2 and BPF3. Unlike what isrequired for bandpass filter in Structure 1, the passband ripples ofBPF1, BPF2, and BPF3 are not critical for good performance as long asthe stopband attenuation is sufficient. In our experience, 30 dBstopband attenuation is adequate. Therefore, low-order IIR filters suchas 2^(nd) or 3^(rd) order Elliptic IIR filters may be used for thisapplication to reduce the hardware and computation complexity.

In contrast to the embodiment illustrated in FIG. 6, the various groupdelays in FIG. 7 must meet the following condition:D _(Δ) ₁ (f)+D _(BPF1)(f)+D _(ADF) _(—) _(FIR)(f)=D _(DAC)(f)+D_(acoustic feedback path)(f)+D _(ADC)(f)  Equation 16The optimal delay Δ₁ in samples can be obtained in the measurement ofthe feedback path during the hearing aid fitting processing. In order toutilize all the ADF coefficients, the delay caused by the adaptivefilter should be minimized. The delay Δ₁ must meet the followingcondition:D _(Δ) ₁ (f)≦D _(DAC)(f)+D _(acoustic feedback path)(f)+D _(ADC)(f)−D_(BPF1)(f)  Equation 17We choose:Δ₁=min{D _(DAC)(f)+D _(acoustic feedback path)(f)+D _(ADC)(f)−D_(BPF1)(f)}_(fεpassband)−ε  Equation 18

Where ε is the tolerance in samples. We typically choose ε equal to 2.

This band-limited feedback cancellation structure does not introduce anyadditional delay in the primary signal path and does not introduceadditional phase distortion to the hearing aid output.

The purpose of the ADF is to estimate the feedback path. In FIG. 7, BPF1is used to limit the bandwidth of the feedback cancellation signal.Because the frequency response of the feedback path has band-passcharacteristics as generally shown in FIG. 21, we may use BPF1 toapproximately match the frequency response of the feedback path. In thisway, the ADF can be used mainly to track the variation of the feedbackpath.

The band-limited adaptive feedback canceller can be implemented on aplatform with either a general-purpose digital signal processor or aspecialized digital signal processor. Due to the size and powerconstraints of hearing aid circuit design, it is desirable to utilize afixed-point digital signal processor with limited precision and wordlength as the adaptive feedback canceller. Thus, the efficient digitalrealization of the band-limited adaptive feedback canceller is extremelycritical for the performance of the feedback cancellation under theconstraint of limited hardware and computational resources. The presentinvention simplifies the computational requirements and addresses issuesassociated with the limited-precision effects on the adaptation process.

In both of the above-described structures of band-limited feedbackcancellers, the operations of adaptive filtering are performed in thesame way. For a fixed-point implementation, some additional modules arerequired to maintain efficiency of calculation under the limitedprecision constraint. A generalized structure for adaptively filtered,band-limited feedback cancellers is shown in FIG. 9. This generalizedstructure is applicable for both of the above-described embodiments.There are three input ports (x₁(n), x₂(n), and e(n)) and one output port(y(n)) for this adaptive filtering configuration.

For the feedback canceller structure shown in FIG. 6:x ₁(n)=x ₂(n)=x(n)

For the feedback canceller structure shown in FIG. 7:x ₁(n)=x(n)x ₂(n)=x′(n)e(n)=e′(n)

The generalized structure contains an adjustable FIR filtering module, apower estimation module, a coefficient adaptation module, a DC removingmodule, a coefficient bandpass filtering (CBF) module and a controlunit. The purposes and detailed implementation of these modules isdescribed below:

1. Adjustable FIR Filtering

The adaptive FIR filter is used to approximate the dynamic feedback pathand generate a feedback cancellation signal by convolving the inputsignal x₁(n) with current filter coefficients {w_(k)(n): 0≦k≦M−1}.However, the feedback path response has a very large dynamic range. Inthe fixed-point implementation, to fully make use of the internalprecision of fixed-point adaptive FIR filtering, we must maximize theADF coefficients to fit the word-precision allocated to them. An ADFscaling gain (G) is used to maximize the ADF coefficients and provide awide dynamic range for the feedback cancellation signal. Therefore, thecalculation of the M-tap adaptive FIR filter output is slightly modifiedas: $\begin{matrix}{{y(n)} = {G \cdot {\sum\limits_{k = 0}^{M - 1}\quad{{w_{k}(n)} \cdot {x_{1}\left( {n - k} \right)}}}}} & \text{Equation~~19}\end{matrix}$

The scaling gain G is selected as a power-of-two number 2^(L) and can beimplemented by left/right shifting. Normally, it is sufficient for L tobe in the range [−3, 3], which provides a dynamic range from −18 dB to18 dB. FIG. 20 shows a functional block diagram of adjustable FIRfiltering with a power-of-two scaling gain.

2. Coefficient Adaptation

With the ADF scaling gain included, the calculation for time-varyingstep-size has to be modified as: $\begin{matrix}{{\mu(n)} = \frac{C}{G \cdot \left\lbrack {{\left( {1 - \rho} \right) \cdot {p(n)}} + {ME}} \right\rbrack \cdot M}} & \text{Equation~~20}\end{matrix}$

As shown in Equation 10 and Equation 13, p(n) is the power estimation ofthe combined signal e(n) and x₂(n). In the fixed-point implementation,because of the word-truncation in calculating ρ−p(n−1), limit cycleswill prevent p(n) from becoming zero, and therefore ME in Equation 20 isnot necessary. For simplicity, we set ME to 0.

In order to avoid the division in calculation of time-varying step-size,we use a power-of-two number to approximate p(n) and select C, (1−ρ), G,and M as power-of-two numbers:

-   -   C=2^(−K)    -   (1−ρ)=2^(−J)    -   G=2^(L)    -   M=2^(F)        Equation 20 can then be rewritten as: $\begin{matrix}        \begin{matrix}        {{\mu(n)} \approx \frac{2^{- K}}{2^{L} \cdot 2^{- J} \cdot 2^{Q{\lbrack{\log_{2}{({p{(n)}})}}\rbrack}} \cdot 2^{F}}} \\        {= 2^{J - K - L - F - {Q{\lbrack{\log_{2}{({p{(n)}})}}\rbrack}}}}        \end{matrix} & \text{Equation~~21}        \end{matrix}$

K is a positive integer to control the adaptation speed. The range of Kis typically from 7 to 10. The smaller value of K provides fasteradaptation speed. J is a positive integer to control the time-constantof power estimation. Typically, we choose 6 for J. L is an integer tocontrol the ADF scaling gain. As stated above, the range is from −3 to+3. L is determined based on the feedback measurement during the hearingaid fitting process so that the filter coefficients of adaptive filterare maximized. F is an integer related to the length of the adaptivefilter. With a sampling rate of 16000 Hz, we choose F=5 (32 taps) sothat the duration of the adaptive filter impulse response is about 2 ms,which is long enough to cover the variation of group delay in thefeedback path in the unstable feedback frequency regions.

Q[ ] is a truncation operation. Q[log₂(p(n))] can be implemented bysearching the position index of the most significant bit (MSB) of p(n).

FIG. 8 shows a functional block diagram of base-2 logarithmquantization. 86 is a positive quantity represented in an unsignedbinary integer format. The position index of the least significant bit(LSB) is 0. Q(log₂(ξ)) returns the position index of the MSB of ε. Whenε is 0, Q[log₂(ε)] returns 0.

We can further simplify the power estimation and coefficient adaptationby using a power-of-two number to approximate the error signal. Thisquantization of error signal does not affect the performance of theadaptive filter. Thus, the power estimation becomes: $\begin{matrix}\begin{matrix}{{p(n)} = {{\left( {1 - \rho} \right) \cdot {p\left( {n - 1} \right)}} + {x_{2}^{2}(n)} + {e^{2}(n)}}} \\{\approx {{p\left( {n - 1} \right)} - {2^{- J} \cdot {p\left( {n - 1} \right)}} + {x_{2}^{2}(n)} +}} \\{{{sign}\left( {e(n)} \right)} \cdot 2^{Q{\lbrack{\log_{2}{({{e{(n)}}})}}\rbrack}} \cdot {e(n)}}\end{matrix} & {{Equation}\quad 22}\end{matrix}$The coefficient adaptation becomes: $\begin{matrix}\begin{matrix}{{{w_{k}\left( {n + 1} \right)} = {{w_{k}(n)} + {{\mu(n)} \cdot {e(n)} \cdot {x_{2}\left( {n - k} \right)}}}},} \\{{{for}\quad 0} \leq k \leq {M - 1}} \\{{\approx {{w_{k}(n)} + {2^{J - K - L - F - {Q{\lbrack{\log_{2}{({p{(n)}})}}\rbrack}}} \cdot}}}\quad} \\{{sign}{\left( {e(n)} \right) \cdot 2^{Q{\lbrack{\log_{2}{({{e{(n)}}})}}\rbrack}} \cdot {x_{2}\left( {n - k} \right)}}} \\{= {{w_{k}(n)} + {{{sign}\left( {e(n)} \right)} \cdot}}} \\{2^{J - K - L - F - {Q{\lbrack{\log_{2}{({p{(n)}})}}\rbrack}} + {Q{\lbrack{\log_{2}{({{e{(n)}}})}}\rbrack}}} \cdot} \\{x_{2}\left( {n - k} \right)}\end{matrix} & {{Equation}\quad 23}\end{matrix}$

Equation 22 shows that only one multiplication is required for the powerestimation. The coefficient adaptation process shown in Equation 23becomes a multiplication-free process and can be implemented withshifting, negation and addition operations.

FIG. 10 shows the functional block diagram for power estimation, andFIG. 11 shows the functional block diagram for a multiplication-freecoefficient adaptation process in which:

-   -   β(n) is the base-2 logarithm quantization of the error signal        e(n);    -   α(n) is the base-2 logarithm quantization of the power        estimation p(n); and    -   v(n) is the sign of the error signal e(n).

Since the band-limited feedback canceller works so efficiently andeffectively in the unstable frequency regions, the adaptation step sizeused for the Normalized LMS adaptive filter may be further reduced tominimize the misadjustment noise and hence improve the hearing aid soundquality. With fixed-point implementation, the normalized LMS adaptationwith a very small step size may be simplified to a sign LMS adaptation.Equation 23 may be rewritten as:w _(k)(n+1)=w _(k)(n)+μsign(e(n)·x ₂(n−k)), for 0≦k≦M−1  Equation 23aWhere μ is a constant. For example, we may choose μ equal to 1 whenw_(k)(n) is represented with a 12-bit integer. By doing so, thecomputations associated with power estimation, MSB search, and shiftingthat are required for the Normalized LMS are eliminated.

3. Limited-Precision Effects Due to Fixed-Point Implementation

In the fixed-point implementation of the adaptive-filtering algorithm,both the inputs and internal algorithmic quantities must be quantized toa certain limited precision. These quantization errors may accumulatewithout bound until overflow occurs, resulting in unacceptableperformance. For example, a slight DC offset in e(n) and x₂(n), whichresults from either the original ADC output or the word-truncation ofband-limiting filtering, may accumulate over time and cause an increaseof DC offset in the adaptive filter coefficients. The truncationoperations in the adaptive filter coefficient adaptation may also causesimilar DC build-up in the adaptive filter coefficients, especially whenthe signal level is low. Furthermore, the low frequency gain of the ADFfilter response may gradually build up if the chosen band-limitingfilter BPF1 has excessive low frequency attenuation compared to thefeedback path. In both cases, the adaptive filter coefficients mayoverflow or saturate. A DC removing module is included to periodicallyremove the DC offset from the adaptive filter coefficient. Anotherbandpass filtering module is provided to filter the adaptive filtercoefficients in order to suppress the low frequency and high frequencyresponse build-up in the adaptive filter response. This operation isonly needed when the filter coefficient is saturated.

In the DC removing module, the following operation is implemented toestimate the DC offset in the filter coefficient and subtract theestimated DC offset from the ADF filter coefficients: $\begin{matrix}{{m(n)} = {\frac{1}{M} \cdot {\sum\limits_{k = 0}^{M - 1}\quad{w_{k}(n)}}}} & {{Equation}\quad 24}\end{matrix}$

FIG. 12 illustrates the computational process for DC removal.

For example, the DC removal may be scheduled every 256 samples at 16000Hz sampling rate.

In the CBF module, a zero-delay bandpass filtering operation on the ADFcoefficients is performed as follows:w _(k)(n+1)=w _(k)(n)/2−w _(k+1)(n)/2,0≦k≦M−3  Equation 26w _(k)(n+1)=w _(k)(n)/2, k=M−2, M−1  Equation 27

FIG. 13 illustrates the computational process for bandpass filtering.This simple bandpass filtering operation doesn't offer a perfectly flat0 dB magnitude response across the passband, and may introduce minoraudible distortion at the hearing aid output. It cannot be appliedfrequently and is only triggered when any one of the ADF coefficients issaturated.

As mentioned earlier, the adaptive filter coefficient adaptation must beperformed in company with DC removing and coefficient bandpass filteringoperations. Since the DC removing and coefficient bandpass filteringoperations don't need to be performed frequently, we schedule only oneof these three operations to be performed at each sample period. FIG. 14is a flow chart of the scheduling process. In this way, the DC removingoperation is performed periodically, and the coefficient bandpassfiltering operation is triggered only when the SAT signal from thecoefficient adaptation module is on.

FIG. 15 is a logical diagram of the control unit, which generates thecontrol signals for the coefficient adaptation module, the DC removalmodule, and the coefficient bandpass filtering module.

EXPERIMENTAL RESULTS

The first test of this invention was performed with a computersimulation. The simulation model was developed in SIMULINK and builtwith a dynamic feedback path. The dynamic feedback path was measured ona KEMAR ear with a clipboard slowly moving toward and away from the ear.Various hearing aid responses for human subjects were used as hearingaid processing for the simulation.

The hearing aid response and the dynamic feedback path were used toderive the open loop transfer function and identify the unstablefeedback frequencies. The unstable feedback frequencies were used toconfigure the feedback canceller, specifically the bandwidth of theband-limiting filters. The tests were made with and without theband-limited adaptive feedback canceller. The maximum stable hearing aidgain was recorded under both conditions. The simulated hearing aidoutputs were also used for subjective evaluation.

The same tests were performed on human subjects with a real-timeprototype digital hearing aid. The open loop transfer function of thehearing aid was determined based on closed loop probe tube measurement.The unstable feedback frequencies were identified from the open looptransfer function and used to configure the band-limited adaptivefeedback canceller. The maximum stable insertion gains were recordedwith and without the adaptive canceller.

The results have shown that the band-limited feedback cancellereffectively eliminates the oscillation and sub-oscillatory feedback andincreases the stable hearing aid insertion gain by 12-15 dB with minimumdistortion to the sound quality.

FIG. 21 shows an example of open loop transfer function measured onKEMAR ear. There are three unstable feedback frequencies as indicted bycross symbols. They are at 2660 Hz, 3260 Hz, and 3960 Hz. Therefore, thecutoff frequency for the band-limiting filters is set to 2460 Hz, whichis about 200 Hz below the lowest unstable feedback frequency.

Alternative Embodiments

The embodiments shown in FIG. 6 and FIG. 7 are two specific examples ofband-limited adaptive feedback cancellers. However, the inventionembraces other embodiments having the same functionality in terms oflimiting the bandwidth of adaptation and bandwidth of the cancellationsignal to the frequency regions known to contain oscillationfrequencies.

For example, in FIG. 6, we can replace the Δ₂-sample delay with twostrictly complementary filters. One filter would be the same as BPF2,whose frequency transfer function is denoted as H₂(f), and the otherwould be its strictly complementary filter SCF2, which has acomplementary frequency transfer function e^(−jΔ) ² ^(2πf)−H₂(f). Suchan embodiment is illustrated in FIG. 16.

We can further combine two identical BPF2s and split the hearing aidprocessing into two processes as shown in FIG. 17. Hearing Aid Process 1is used to process signals in the frequency regions covered by BPF2, andHearing Aid Process 2 is used to process the signals produced by BPF2'scomplementary filter, SCF2. Since the output bandwidth of hearing aidprocess 1 is the same as BPF2, the need for BPF1 as shown in FIG. 6 iseliminated. A linear-phase FIR filter is selected for BPF2 and itsstrictly complementary filter is selected for SCF2 in order to minimizephase distortion in the primary signal path of the hearing aid. For somehearing aid applications, the phase distortion in the primary signalpath can be either tolerated or corrected by other hearing aidprocessing modules. In this case, we can relax the strictlycomplementary condition to other kinds of complementary conditions,e.g., power complementary so that infinite-impulse-response (IIR)filters may be used to replace BPF2 and SCF2 to further reduce thehardware and computational complexity.

So far, we have assumed that an analog automatic gain control (AGC) isused in the hearing aid between the hearing aid microphone and theanalog-to-digital converter. Since the AGC is part of the feedback pathbut not part of the cancellation signal path, the sudden gain change ofAGC due to a sharp transition of the hearing aid input signal maydegrade the performance of the cancellation. One alternate construction,as shown in FIG. 18, is to move the AGC after the feedback cancellationjunction so that the AGC is in both the feedback path and thecancellation path. This would require a digital implementation of AGC.Another alternate solution, as shown in FIG. 19, is to digitally applythe AGC gain to the feedback cancellation signal so that the feedbackcancellation signal tracks the AGC gain change. This method wouldrequire converting the AGC gain to a digital format.

The band-limited feedback canceller offers the best sound quality whenthe cancellation bandwidth is minimized. As is known, the oscillationfrequencies of a hearing aid are functions of the hearing aid gain,which is normally controlled by the hearing aid volume control. Thus,the cancellation bandwidth of the feedback canceller can also becontrolled by the hearing aid volume control in order to achieve thebest sound quality. This can be accomplished by storing several sets offilter coefficients for the band-limiting filter in the hearing aid.With any given hearing aid volume control setting, the appropriate setof filter coefficients is used to provide a filter response that coversall the oscillation frequencies and has the minimum bandwidth. Thisfilter selection process is needed only when the hearing aid wearerchanges the volume control setting.

We may also choose different constant K to control the adaptation speedfor different hearing aid volume control settings, since the higherhearing aid gain setting may require a faster adaptation speed tosuppress the feedback.

It will be recognized that the above described invention may be embodiedin other specific forms without departing from the spirit or essentialcharacteristics of the disclosure. Thus, it is understood that theinvention is not to be limited by the foregoing illustrative details,but rather is to be defined by the appended claims.

1. A feedback canceller for an audio amplification device comprising: anadaptive filter comprising means for convolving? an input of theadaptive filter with filter coefficients; means for combining an outputof the adaptive filter with an input of the audio amplification device;a first band limiting filter having an input coupled to an output of theaudio amplification device and an output coupled to the input of theadaptive filter, wherein the first band limiting filter has a passbandlimited to a frequency band containing unstable frequencies; a secondband limiting filter having an input coupled to the input of the audioamplification device and an output; a third band limiting filter havingan input coupled to the output of the first band limiting filter and anoutput; wherein the second and third band limiting filters havepassbands limited to the frequency band containing unstable frequenciesand the filter coefficients are functions of the outputs of the secondand third band limiting filters.
 2. The device of claim 1 wherein thesecond and third band limiting filters have matching phase responses. 3.The device of claim 1 wherein the second and third band limiting filtershave substantially identical characteristics.
 4. A method for cancellingfeedback in an audio amplification device comprising the steps of:deriving an open loop transfer function K(f)β(f) of the audioamplification device; calculating all unstable frequencies fu satisfyingthe conditions:|K(f _(u))·β(f _(u))|≧1∠K(f _(u))β(f _(u))=n×360°where K(fu) is thesignal processing circuitry transfer function of the audio amplificationdevice, and where β(fu) is the transfer function of a feedback path;defining an unstable frequency domain containing all f_(u) bounded at alow cutoff frequency established in accordance with a lowest f_(u);applying an output of the audio amplification device to a first bandlimiting filter having a passband limited to the unstable frequencydomain; applying an output of the first band limiting filter to anadaptive filter; combining an output of the adaptive filter with aninput of the audio amplification device.
 5. The method of claim 4wherein the adaptive filter is implemented by a method comprising thesteps of: estimating power of a feedback cancellation error signal andan input signal to the adaptive filter; adapting filter coefficients inaccordance with the estimated power; removing a DC offset from theadapted filter coefficients; bandpass filtering the adapted filtercoefficients; applying the adapted filter coefficients to an adjustablefilter.
 6. The method of claim 5 wherein the step of removing a DCoffset is performed less frequently than the step of adapting filtercoefficients.
 7. The method of claim 5 wherein the step of bandpassfiltering the adapted filter coefficients is performed only when anadapted filter coefficient exceeds a predetermined threshold.
 8. Themethod of claim 5 wherein the step of adapting filter coefficientscomprises shifting, negation and addition without multiplication.
 9. Themethod of claim 5 wherein the adaptive filter is implemented by a methodcomprising the step of convolving the output of the bandpass filter withfilter coefficients.
 10. The method of claim 9 wherein the method ofimplementing the adaptive filter further comprises the step of applyinga scaling gain to the filter coefficients.
 11. The method of claim 10wherein the scaling gain is a power of
 2. 12. The method of claim 11wherein the scaling gain is in the range of 2⁻³ to 2³.
 13. The method ofclaim 4 wherein the audio amplification device comprises a hearing aidamplifier.
 14. The method of claim 13 further comprising the step ofmeasuring adaptive filter coefficients with the hearing aid inserted inan ear of a wearer to identify unstable frequencies.
 15. The method ofclaim 4 wherein the first band limiting filter is a high pass filter.16. The method of claim 15 wherein the passband of the high pass filterhas a cutoff frequency approximately 200 Hz below the lowest f_(u). 17.The method of claim 4 further comprising the step of delaying the outputof the audio amplification device prior to application to the first bandlimiting filter.
 18. The method of claim 17 wherein the output of theaudio amplification device is delayed by an amount of time that is afunction of a feedback path delay.
 19. The method of claim 4 furthercomprising the step of applying automatic gain control (AGC) to theinput of the audio amplification device.
 20. The method of claim 19wherein AGC is applied after the output of the adaptive filter iscombined with the input of the audio amplification device.
 21. Themethod of claim 19 wherein AGC is applied to both the input of the audioamplification device and the output of the adaptive filter.
 22. Themethod of claim 4 further comprising the step of adjusting an adaptationspeed of the adaptive filter.
 23. The method of claim 22 wherein theadaptation speed is adjusted as a function of a gain of the audioamplification device.
 24. The method of claim 4 further comprising thestep of selecting a length of the adaptive filter.
 25. The method ofclaim 24 wherein the length of the adaptive filter is selected as afunction of sampling rate and the frequency band containing unstablefrequencies so that duration of the adaptive filter's impulse responseis long enough to cover an expected range of variation of group delay inthe frequency band containing unstable frequencies in a feedback pathfrom the output of the audio amplification device to the input thereof.26. The method of claim 4 further comprising the step of matching afrequency response of the first band limiting filter to a frequencyresponse of a feedback path from the output of the audio amplificationdevice to the input thereof.
 27. The method of claim 4 furthercomprising the step of storing a plurality of sets of filtercoefficients for the first band limiting filter.
 28. The method of claim27 further comprising the step of selecting a set of filter coefficientsas a function of a gain of the audio amplification device.
 29. Themethod of claim 5 wherein the step of bandpass filtering the adaptedfilter coefficients applies a passband limited to a frequency bandcontaining unstable frequencies.
 30. A feedback canceller for a hearingaid amplifier comprising: means for creating a first delay having aninput coupled to an audio output of the hearing aid and an output; afirst band limiting filter having an input coupled to the output of thefirst delay means and an output; an adaptive filter having an inputcoupled to the output of the first band limiting filter and an output;means for creating a second delay having an input coupled to aconditioned output of a hearing aid microphone and an output; a firstsumming node having a non-inverting input coupled to the output of thesecond delay means, an inverting input coupled to the output of theadaptive filter and an output coupled to an input of a hearing aidprocessor; a second band limiting filter having an input coupled to theinput of the second delay means and an output; a second summing nodehaving a non-inverting input coupled to the output of the second bandlimiting filter, an inverting input coupled to the output of theadaptive filter and an output; means for selecting a filter coefficienthaving a first input coupled to the output of the first band limitingfilter, a second input coupled to the output of the second summing nodeand an output for supplying the filter coefficient to the adaptivefilter; wherein the first and second band limiting filters havepassbands limited to a frequency band containing all unstablefrequencies of the hearing aid amplifier and wherein a low cutofffrequency of the passbands is established in accordance with a lowest ofthe unstable frequencies.
 31. A feedback canceller circuit for a hearingaid amplifier comprising: means for creating a delay having an inputcoupled to an audio output of the hearing aid and an output; a firstband limiting filter having an input coupled to the output of the delaymeans and an output; an adaptive filter having an input coupled to theoutput of the first band limiting filter and an output; a summing nodehaving a non-inverting input coupled to a conditioned output of ahearing aid microphone, an inverting input coupled to the output of theadaptive filter and an output coupled to an input of a hearing aidprocessor; a second band limiting filter having an input coupled to theoutput of the summing node and an output; a third band limiting filterhaving an input coupled to the output of the first band limiting filterand an output; means for selecting a filter coefficient having a firstinput coupled to the output of the second band limiting filter and asecond input coupled to the output of the third band limiting filter andan output for supplying the filter coefficient to the adaptive filter;wherein the first, second and third band limiting filters have passbandslimited to a frequency band containing all unstable frequencies of thehearing aid amplifier and wherein a low cutoff frequency of thepassbands is established in accordance with a lowest of the unstablefrequencies.
 32. A feedback canceller circuit for an audio amplificationdevice comprising: means for creating a delay having an input coupled toan audio output of a hearing aid circuit and an output; a first bandlimiting filter having an input coupled to the output of the delay meansand an output; an adaptive filter having an input coupled to the outputof the first band limiting filter and an output; a summing node having anon-inverting input coupled to a conditioned output of a hearing aidmicrophone, an inverting input coupled to the output of the adaptivefilter and an output coupled to the input of the hearing aid processingmodule; a second band limiting filter having an input coupled to theoutput of the summing node and an output; a third band limiting filterhaving an input coupled to the output of the first band limiting filterand an output; means for selecting a filter coefficient having a firstinput coupled to the output of the second band limiting filter and asecond input coupled to the output of the third band limiting filter andan output for supplying the filter coefficient to the adaptive filter;wherein the first, second and third band limiting filters have passbandslimited to a frequency band containing unstable frequencies; wherein thesecond and third band limiting filters have matching phase responses.33. The device of claim 32 wherein the second and third band limitingfilters have substantially identical characteristics.